Management strategies for a defined contribution pension fund under the hybrid stochastic volatility model

Abstract

In this paper, we introduce the Heston-Hull-White (the hybrid) model in the pension fund management. The optimal investment and benefit payments policies for the DC pension fund with an income drawdown option are presented explicitly. In this study, the pension fund manager is allowed to invest the fund wealth in riskless and risky assets. The risk asset price dynamics evolve according to the Hybrid Stochastic Volatility (Heston-Hull-White) model. The goal of the pension fund manager is to maintain the standard of lives for the pension fund members after retirement. We derived the HJB equation and established the closed-form solution for the optimal control policies using stochastic dynamic programming principle. To illustrate the economic implications of the model, we provide a numerical example and simulations. The results reveal that the optimal investment and benefit payments strategies convergence successful with time t. The risk asset price volatility and interest rate mean reversion are inversely proportional to investment policy. The interest rate volatility and risk preference are both directly proportional to investment and benefit payments. The pension fund managers are advised to control the investment and the benefit payments policies to achieve the goals of the pension fund members.

Optimal Investment Strategies for DC-Pension Fund under Combined Stochastic Volatility Models

“…"The demographic advancement that affects the sustainability of retirement income and the subsequent evolution of equity market has increased adoption of the subject. The benefit payments depend on the fund portfolio and the efficiency of the investment strategy" [1]. "In the classical work of Merton dynamics portfolio selection model, return rates and volatilities of risk assets are all assumed to be deterministic" [2,3].…”

“…𝐿𝑒𝑡 𝑄 ̂(𝑡, 𝑣, 𝑟, 𝑥) ∈ 𝐶 (1,2,2,2) ([0, 𝑇] × 𝑅 × 𝑅 × 𝑅) 𝑤ℎ𝑒𝑟𝑒 𝐶 (1,2,2,2) ([0, 𝑇] × 𝑅 × 𝑅 × 𝑅) is the space function that are continuously differentiable with respect to𝑡 ∈ [0, 𝑇] and twice continuously differentiable with respect to (𝑣, 𝑟, 𝑥) ∈ (𝑅 × 𝑅 × 𝑅).…”

Sharpe-Ratio Portfolio in Controllable Markov Chains: Analytic and Algorithmic Approach for Second Order Cone Programming

“…Vazquez and Clempner [19] developed a portfolio technique based on a Lagrangian regularization method. The literature differs depending on whether you use continuous or discrete time, a finite or infinite horizon, and so on [20][21][22][23][24][25][26].…”

Robust mean-variance efficient strategies of DC pension plans with ambiguity under stochastic interest rate and stochastic volatility

“…It can be seen that the DC pension plan is more in line with the management status of pension plans. In recent years, a large number of scholars have studied the optimal investment strategies of DC pension plans under the expected utility maximizing criterion, for example, Guan and Liang (2014), Tang et al (2018), Mwanakatwe et al (2019) and Ma et al (2020). In order to better reflect the attitude of pension plan managers toward risk, Guan and Liang (2016) considered the risk management of DC pensions under loss aversion and Value-at-Risk constraints.…”